Even though the integer quantum Hall transition has been investigated for nearly four decades its critical behavior remains a puzzle. The best theoretical and experimental results for the localization length exponent ν differ significantly from each other, casting doubt on our fundamental understanding. While this discrepancy is often attributed to long-range Coulomb interactions, Gruzberg et al. [Phys. Rev. B 95, 125414 (2017)10.1103/PhysRevB.95.125414] recently suggested that the semiclassical Chalker-Coddington model, widely employed in numerical simulations, is incomplete, questioning the established central theoretical results. To shed light on the controversy, we perform a high-accuracy study of the integer quantum Hall transition for a microscopic model of disordered electrons. We find a localization length exponent ν=2.58(3) validating the result of the Chalker-Coddington network.
M. Puschmann et al., "Integer Quantum Hall Transition on a Tight-Binding Lattice," Physical Review B, vol. 99, no. 12, American Physical Society (APS), Mar 2019.
The definitive version is available at https://doi.org/10.1103/PhysRevB.99.121301
Keywords and Phrases
Critical behavior; High-accuracy; Localization length; Long-range Coulomb interaction; Microscopic modeling; Quantum hall; Tight binding
International Standard Serial Number (ISSN)
Article - Journal
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01 Mar 2019